(356g) Multi-Site, Multi-Pollutant Atmospheric Data Analysis Using Riemannian Geometry

Air pollution is a serious threat to human health and the environment [1,2]. To develop effective mitigation policies and technological solutions, it is essential to monitor and model atmospheric pollutant behavior. Traditional air pollution monitoring is done through spatially-distributed monitoring stations that provide accurate measurements of multiple atmospheric pollutants at high temporal resolution. Historically, air pollution research and policy has focused on controlling individual pollutants due to the complexity of analyzing and modeling multi-pollutant data. However, there is a growing recognition of the need for air quality management tools and methods that integrate multi-pollutant data to estimate health risks and environmental impacts of complex mixtures of air pollutants [3,4].

To analyze spatio-temporal relationships between pollutants, multivariate time series data is often encoded as covariance matrices [5,6]. However, the commonly used methods to analyze these matrices assume that the data lies in a Euclidean space, which can miss relevant geometric structure in the data [7,8]. Furthermore, many of these methods are based on single pollutant monitoring or on a single monitoring location and do not account for dynamic relationships between different pollutants across varying monitoring sites.

To overcome these limitations, we present a new analysis framework that extends existing methods for use in multi-pollutant, multi-site monitoring. The framework exploits the observation that covariance matrices lie on a Riemannian manifold, which represents a space governed by non-Euclidean geometry [7,8]. Accounting for the curvature of the Riemannian manifold allows for computation of relationships that respect the data's high-dimensional structure and prevents physically inconsistent results of data analysis [7,9]. We demonstrate the benefits of incorporating Riemannian geometry through an analysis of real, multi-pollutant data taken from 34 air quality monitoring sites in Beijing, China.

This presentation provides a practical introduction to the mathematics of the Riemannian geometry of covariance matrices and demonstrates the benefits of incorporating this geometry into the analysis of multi-pollutant, multi-site monitoring data. The proposed framework has the potential to improve outcomes of multivariate data analysis methods and aid in the development of effective air pollution mitigation policies and technological solutions.

References:

1.) Kampa, Marilena, and Elias Castanas. "Human health effects of air pollution." Environmental pollution 151.2 (2008): 362-367.

2.) Mayer, Helmut. "Air pollution in cities." Atmospheric environment 33.24-25 (1999): 4029-4037.

3.) Dominici, Francesca, et al. "Opinion: Protecting Human Health From Air Pollution: Shifting From a Single-pollutant to a Multipollutant Approach." Epidemiology (2010): 187-194.

4.) U. EPA. The multi-pollutant report: Technical concepts and examples, 2007.

5.) Statheropoulos, M., N. Vassiliadis, and A. Pappa. "Principal component and canonical correlation analysis for examining air pollution and meteorological data." Atmospheric environment 32.6 (1998): 1087-1095.

6.) von Schneidemesser, Erika, et al. "Toxic metals in the atmosphere in Lahore, Pakistan." Science of the Total Environment 408.7 (2010): 1640-1648.

7.) Smith, Alexander, et al. "Data analysis using Riemannian geometry and applications to chemical engineering." Computers & Chemical Engineering 168 (2022): 108023.

8.) Pennec, Xavier, Pierre Fillard, and Nicholas Ayache. "A Riemannian framework for tensor computing." International Journal of computer vision 66 (2006): 41-66.

9.) Sommer, Stefan, et al. "Manifold valued statistics, exact principal geodesic analysis and the effect of linear approximations." Computer Vision–ECCV 2010: 11th European Conference on Computer Vision, Heraklion, Crete, Greece, September 5-11, 2010, Proceedings, Part VI 11. Springer Berlin Heidelberg, 2010.